Finite Group DatabasebetaFinite Group DatabasebetaOrder 1152.
385 conjugacy classes of subgroups; only the 76 normal subgroups are shown.
This group has 385 conjugacy classes of subgroups — too many to draw. Only its 76 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. #10592892 | C2 | semidirect |
| 2. C3×#5196 | C2 | semidirect |
| 3. C3×#5193 | C2 | semidirect |
| 4. #10590880 | C2 | semidirect |
| 5. #10589134 | C2 | semidirect |
| 6. #10589128 | C2 | semidirect |
| 7. #10589126 | C2 | semidirect |
| 27. #5196 | D3 | semidirect |
| 31. #5193 | D3 | semidirect |
| 44. C32×Q16 | D4 | semidirect |
| 46. C32×D8 | D4 | semidirect |
| 133. C3×Q16 | D12 | semidirect |
| 134. C3×Q16 | #67 | semidirect |
| 141. C3×D8 | D12 | semidirect |
| 142. C3×D8 | #67 | semidirect |
| 253. Q16 | #626 | semidirect |
| 261. D8 | #626 | semidirect |
| 297. C32 | #2213 | semidirect |
| 341. C3 | #70926 | semidirect |
| 342. C3 | #71514 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #10592892 | 2 |
| C3×#5196 | 2 |
| C3×#5193 | 2 |
| #10590880 | 2 |
| #10589134 | 2 |
| #10589128 | 2 |
| #10589126 | 2 |
| #71514 | 3 |
| #70926 | 3 |